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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(x)/(2*tan(x)^2+2)+x/2

¿Cómo vas a descomponer esta tan(x)/(2*tan(x)^2+2)+x/2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    tan(x)      x
------------- + -
     2          2
2*tan (x) + 2
x2+tan⁡(x)2tan⁡2(x)+2\frac{x}{2} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} 
tan(x)/(2*tan(x)^2 + 2) + x/2
Simplificación general [src] 
x   sin(2*x)
- + --------
2      4
x2+sin⁡(2x)4\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4} 
x/2 + sin(2*x)/4
Respuesta numérica [src] 
0.5*x + tan(x)/(2.0 + 2.0*tan(x)^2)
0.5*x + tan(x)/(2.0 + 2.0*tan(x)^2)
Combinatoria [src] 
         2            
x + x*tan (x) + tan(x)
----------------------
     /       2   \    
   2*\1 + tan (x)/
xtan⁡2(x)+x+tan⁡(x)2(tan⁡2(x)+1)\frac{x \tan^{2}{\left(x \right)} + x + \tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} 
(x + x*tan(x)^2 + tan(x))/(2*(1 + tan(x)^2))
Unión de expresiones racionales [src] 
  /       2   \         
x*\1 + tan (x)/ + tan(x)
------------------------
      /       2   \     
    2*\1 + tan (x)/
x(tan⁡2(x)+1)+tan⁡(x)2(tan⁡2(x)+1)\frac{x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} 
(x*(1 + tan(x)^2) + tan(x))/(2*(1 + tan(x)^2))
Potencias [src] 
                 /   I*x    -I*x\           
x              I*\- e    + e    /           
- + ----------------------------------------
2   /                      2\               
    |      /   I*x    -I*x\ |               
    |    2*\- e    + e    / | / I*x    -I*x\
    |2 - -------------------|*\e    + e    /
    |                    2  |               
    |      / I*x    -I*x\   |               
    \      \e    + e    /   /
x2+i(−eix+e−ix)(−2(−eix+e−ix)2(eix+e−ix)2+2)(eix+e−ix)\frac{x}{2} + \frac{i \left(- e^{i x} + e^{- i x}\right)}{\left(- \frac{2 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 2\right) \left(e^{i x} + e^{- i x}\right)} 
x/2 + i*(-exp(i*x) + exp(-i*x))/((2 - 2*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x)))
Parte trigonométrica [src] 
x           sin(x)        
- + ----------------------
2   /         2   \       
    |    2*sin (x)|       
    |2 + ---------|*cos(x)
    |        2    |       
    \     cos (x) /
x2+sin⁡(x)(2sin⁡2(x)cos⁡2(x)+2)cos⁡(x)\frac{x}{2} + \frac{\sin{\left(x \right)}}{\left(\frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right) \cos{\left(x \right)}} 
x               sec(x)            
- + ------------------------------
2   /          2     \            
    |     2*sec (x)  |    /    pi\
    |2 + ------------|*sec|x - --|
    |       2/    pi\|    \    2 /
    |    sec |x - --||            
    \        \    2 //
x2+sec⁡(x)(2sec⁡2(x)sec⁡2(x−π2)+2)sec⁡(x−π2)\frac{x}{2} + \frac{\sec{\left(x \right)}}{\left(\frac{2 \sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 2\right) \sec{\left(x - \frac{\pi}{2} \right)}} 
x   sin(2*x)
- + --------
2      4
x2+sin⁡(2x)4\frac{x}{2} + \frac{\sin{\left(2 x \right)}}{4} 
x           sec(x)        
- + ----------------------
2   /         2   \       
    |    2*sec (x)|       
    |2 + ---------|*csc(x)
    |        2    |       
    \     csc (x) /
x2+sec⁡(x)(2+2sec⁡2(x)csc⁡2(x))csc⁡(x)\frac{x}{2} + \frac{\sec{\left(x \right)}}{\left(2 + \frac{2 \sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}} 
               /pi    \        
            csc|-- - x|        
x              \2     /        
- + ---------------------------
2   /         2/pi    \\       
    |    2*csc |-- - x||       
    |          \2     /|       
    |2 + --------------|*csc(x)
    |          2       |       
    \       csc (x)    /
x2+csc⁡(−x+π2)(2+2csc⁡2(−x+π2)csc⁡2(x))csc⁡(x)\frac{x}{2} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\left(2 + \frac{2 \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}} 
x        tan(x)    
- + ---------------
2     /       2   \
    2*\1 + tan (x)/
x2+tan⁡(x)2(tan⁡2(x)+1)\frac{x}{2} + \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} 
x       1     
- + ----------
2   4*csc(2*x)
x2+14csc⁡(2x)\frac{x}{2} + \frac{1}{4 \csc{\left(2 x \right)}} 
               /    pi\        
            cos|x - --|        
x              \    2 /        
- + ---------------------------
2   /         2/    pi\\       
    |    2*cos |x - --||       
    |          \    2 /|       
    |2 + --------------|*cos(x)
    |          2       |       
    \       cos (x)    /
x2+cos⁡(x−π2)(2+2cos⁡2(x−π2)cos⁡2(x))cos⁡(x)\frac{x}{2} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\left(2 + \frac{2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos{\left(x \right)}} 
                2           
x          2*sin (x)        
- + ------------------------
2   /         4   \         
    |    8*sin (x)|         
    |2 + ---------|*sin(2*x)
    |       2     |         
    \    sin (2*x)/
x2+2sin⁡2(x)(8sin⁡4(x)sin⁡2(2x)+2)sin⁡(2x)\frac{x}{2} + \frac{2 \sin^{2}{\left(x \right)}}{\left(\frac{8 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 2\right) \sin{\left(2 x \right)}} 
x          1       
- + ---------------
2        /      pi\
    4*sec|2*x - --|
         \      2 /
x2+14sec⁡(2x−π2)\frac{x}{2} + \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} 
x        cot(x)    
- + ---------------
2     /       2   \
    2*\1 + cot (x)/
x2+cot⁡(x)2(cot⁡2(x)+1)\frac{x}{2} + \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} 
x            1          
- + --------------------
2   /       2   \       
    |2 + -------|*cot(x)
    |       2   |       
    \    cot (x)/
x2+1(2+2cot⁡2(x))cot⁡(x)\frac{x}{2} + \frac{1}{\left(2 + \frac{2}{\cot^{2}{\left(x \right)}}\right) \cot{\left(x \right)}} 
       /      pi\
    cos|2*x - --|
x      \      2 /
- + -------------
2         4
x2+cos⁡(2x−π2)4\frac{x}{2} + \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} 
x/2 + cos(2*x - pi/2)/4
Denominador racional [src] 
             /         2   \
2*tan(x) + x*\2 + 2*tan (x)/
----------------------------
                2           
       4 + 4*tan (x)
x(2tan⁡2(x)+2)+2tan⁡(x)4tan⁡2(x)+4\frac{x \left(2 \tan^{2}{\left(x \right)} + 2\right) + 2 \tan{\left(x \right)}}{4 \tan^{2}{\left(x \right)} + 4} 
(2*tan(x) + x*(2 + 2*tan(x)^2))/(4 + 4*tan(x)^2)
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